Question

simplifique cada expressão
a) (1/2)^3 vezes (1/2)^ -2 Sobre (1/2)^ -6
b) 16^2 vezes 18^3 sobre 2^9
c) X^10 vezes (x^2)^4 sobre x^3:x^2
d) 5^3x-2 vezes 5^ x-1 sobre 5^ x-5

Answer 1

a) $( \frac{1}{2})^{3} * ( \frac{1}{2})^{-2} * ( \frac{1}{2})^{-6} = ( \frac{1}{2})^{(3-2-6)} = ( \frac{1}{2})^{-5} = 2^{5} = 32$

b) $16^{2} * 18^{3} * 2^{9} = (2^{4})^{2}*2^{9}*(2*9)^3 = 2^{8}*2^{9}*2^{3}*9^{3} = 2^{(8+9+3)} * 9^{3}$ $= 2^{20} * 9^{3} = 1.048.576 * 729 = 764.411.904$

c) $\frac{x^{10}*(x^{2})^{4}}{\frac{x^{3}}{x^{2}}} = \frac{x^{10}*x^{8}}{x^{3}*x^{-2}}= \frac{x^{18}}{x} = x^{17}$

d) $5^{(3x-2)} * 5^{(x-1)} * 5^{(x-5)} = 5^{(3x-2+x-1+x-5)} = 5^{(5x-8)}$